EPIPOLAR RESAMPLING OF HIGH RESOLUTION SATELLITE IMAGERY

Transcription

1 EPIPOLAR RESAMPLING OF HIGH RESOLUTION SATELLITE IMAGERY Tetsu Ono, Gaduate Schoo of Engineeing, Koto Univesit, Yoshida-Honmachi, Sako-ku, Koto , JAPAN, ABSTRACT This pape pesents a pactica method of epipoa esamping of high-esoution sateite image. Sateite image imaged with a inea aa CCD senso has quite diffeent geometic chaacteistics fom aeia photogaphs, theefoe the conventiona method of epipoa esamping is not appicabe to it. On the othe hand, epipoa esamping method based on igoous oientation mode with high geometic fideit becomes too compicated and then is not suitabe pactica use. In ode to ovecome this pobem, the autho poposes to app the we-estabished 2D affine oientation mode to the epipoa esamping of sateite image. Fist, this pape ough mentions the chaacteistics of this mode. Then it is shown how the mode is suitab appicabe to epipoa esamping. Second, the pape poposes the impoved method that does not equie an DTM o igoous geometic paametes fo eduction of vetica paaaes. Fina an epeiment vaidates the poposed method with SPOT image, whee the RMS vaue of vetica paaaes between a pai of steeo epipoa images was ess than haf a pie. KEYWORDS: Epipoa Resamping, High-Resoution Sateite Image, CCD ine scanne image, 2D Affine Oientation Mode, Affine Tansfomation 1. INTRODUCTION High-esoution sateite image is epected to be a majo souce of 3D measuement of gound in the nea futue. Especia automatic steeo potting to geneate DTMs b steeo matching technoog is high equied. Howeve, the pojection of sateite image, which is imaged with a CCD ine senso, is quite diffeent fom that of conventiona aeia photogaphs. This eads to faiue of appication of we-known epipoa geomet. CCD ine scanne image is not chaacteized b igoous thee dimentiona pespective pojection in a soid fame, but two-dimensiona sequentia pespective pojection in a ine. It is aead epoted that stict epipoa images cannot be geneated fom SPOT image without DTMs (Otto, 1988). The same appies to high-esoution sateite image with CCD ine scanne. Fo this eason, sevea pocedues which geneate pseudo epipoa image b using DTMs have been pesented. 1. In ode to geneate coase pseudo epipoa image, each pie of sateite image is pojected on a hoizonta pane ocated at an aveage teain height. A pai of the pseudo epipoa images has sti age vetica paaaes (Haaa, 1998). If DTMs of the coesponding aea eist, the sateite images ae pojected onto the DTMs and epojected onto a new image pane aong epipoa ine (O Nei et a, 1988). The idea of this method is ve simpe and appicabe to eve oientation mode. The pocedues, howeve, ae compicated fo pactica puposes. 2. The epipoa images ae esamped unde the assumption that a time-vaiant factos inea affect to sateite image (Otto, 1988). The eationship between height diffeences and vaue of vetica paaaes can be descibed b an equation. This pocedue is not quite compicated as fa as non-inea effects ae not consideed. Both of the pocedues cannot achieve pactica accuac without high pecise oientation paametes. In this stud, the autho poposes an atenate method to geneate epipoa image, which is ve simpe, high accuate and does not equie the igoous oientation paametes no DTMs.

2 2. GEOMETRIC CHARACTERISTICS OF HIGH-RESOLUTION SATELLITE IMAGERY In compaison with mid esoution (m-10m on the gound) sateite image such as SPOT, 1m highesoution sateite image has a much naowe fied ange. This means that the pojection of images is nea appoimated b paae athe than centa one. If conventiona oientation paametes ae used, ve high coeation between them occus. A high-esoution sateite image coves a ve sma gound aea in singe scene, which is imaged in a shot time span on obit. The movement of the sateite can be appoimate epessed b inea function and its attitude paametes ae epected to be amost constant duing the shot peiod. 3. 2D AFFINE ORIENTATION MODEL 3.1 The Basic Equations Okamoto (1999) poposed the oientation theo of CCD ine senso image based on 2D affine pojection. The mode named 2D affine oientation mode can be deived fom conventiona coineait equation b consideation of situation mentioned in the pevious section. Each ine of an image is imaged b one-dimensiona centa pespective, and each has diffeent eteio oientation. Let eteio oientation paametes fo ine numbe i be epessed b coodinates of the pojection cente Xoi, Yoi, Zoi and anges φ i,ω i, κ i. These paametes ae time vaiant. Man studies have indicated that the sateite senso geomet can be modeed b eiptica obit and in this case its attitude paametes can be epessed with ponomias. The effect of eath otation and eath cuvatue must be consideed. The coineait equation is descibed as: 0 = λ c ( R R R ) φi ωi κi T X X Y Y Z Z oi oi oi whee (X,Y,Z) is the gound coodinates of an object point, λ is scae paamete, c is pincipa distance, is coodinate of image point and Rφi, Rωi, Rκi ae otation maties. Now that the scene is pojected to the image b paae pojection, c can be set to infinit. The thid (1) equation in Equation 1 oses the meaning and the equation can be descibed as foows: 0 = a11(x-xoi) + a12(y-yoi) + a13(z-zoi) (2) = a22(x-xoi) + a23(y-yoi) + a23(z-zoi) (3) whee aij (i=1,2; j=1,2,3) ae eements of the mati λ(rφirωirκi) T. We assume futhe that the senso moves inea in space and the attitude does not change. The pojection cente in each ine is descibed as foows: Xoi = Xo + X i With Xo and X being constant vaue. The simia epessions ae defined ikewise fo Yoi and Zoi. Line numbe i is epessed b Equation 2 and these ones. a i = ( X X a ) + a X + a ( Y Y ) + a Y + a Z ( Z Z 11 o 12 o 13 o ) (4) Now, ine numbe i can be epaced b image coodinate. Assuming that the attitude does not change, aij ae egaded as constant paametes. Equation 4 aanged fo the constant coefficients is descibed b agebaic epession. = A + () 1X + A2Y + A3 Z A4 Equation 3 is aso epessed b simia aangement. = A + (6) X + A6Y + A7 Z A8 whee Ai (i=1,,8 ) ae independent coefficients. Equation and 6 descibe the coineait eationship between the coodinates (,) of 2D affine image and gound coodinates (X,Y,Z). 3.2 Image Tansfomation In eait, sateite images ae taken centapespective in scanning diection. Fo igoous anasis, the affine image coodinate must be tansfomed to the coesponding oigina image coodinate p. The eationship between p and at pain fied is given in the fom (Okamoto et a, 1992) = /( 1 (tanω) / c) (7) p p

3 Fig. 1. Tansfomation of a centa-pespective ine image into an affine one Howeve, at hi aea o mountainous aea, we cannot ignoe the image tansfomation eos due to height diffeences in the teain. Let Z indicate height diffeence of a gound point fom the aveage height and α denote the haf of the fied ange of the scanne. The image tansfomation eo due to negecting the height diffeence Z is descibed as foows (Okamoto et a, 1992): = Z(tan( ω + α) tanω) cosω (8) The mode based on affine pojection can epess an ine movement and distotion eating to the images. Athough the mode is deived unde the assumption that the attitude of senso does not change duing the acquisition of one scene image, sma changes of attitude paametes can be aso estimated b the mode as fa as the effects ae egaded as appoimate inea. Unde the geometica pecuia condition of high-esoution sateite images, the attitude paametes high coeate to the movement paametes. Fo eampe, sma changes of φ ae ve simia to changes of Zo. Sma changes of ω ae amost same as changes of Xo and Yo. Because the attitude of sateite is stabe, the effects can be embodied as inea movement o distotion in the affine images. The effects of eath cuvatue and eath otation ae aso estimated with them in sma aea. Moeove, this mode is capabe of geometica pepocessed images (e.g., SPOT Leve-1B), because the mode does not teat the geometic oientation paametes diect and then the mode aows defomed images as fa as the defomations ae inea. The mode is appicabe fo even the otated images o fipped images. This chaacteistic is ve impotant fo the epipoa esamping method in this stud. 4. THE PRIMARY THEORY OF EPIPOLAR RESAMPLING FOR AFFINE IMAGES 4.1 Epipoa Geomet of Affine Image Fig. 2. Image Tansfomation Eo Due to Negecting Height Diffeence in the Teain 3.3 Chaacteistics of 2D Affine Oientation Mode 2D affine oientation mode has on 8 agebaic paametes and the basic equations ae inea with espect to the object space coodinates. Theefoe, it is ve simpe, stabe and fast fo mapping pocessing. The paae pojection can be epessed as the centa pespective pojection with infinit foca ength. Accoding, we can sa that the affine pojection is a specia case of the centa pespective pojection. Fo this eason, epipoa geomet of the affine images is consideed b same appoach as that of the centa pespective pojection images. The we-known epipoa geomet is iustated b Fig. 3. The epipoa pane is defined as a pane in which the pojection cente of eft image, that of ight images and an object point ie. The pojection cente of each image is on one, thus the epipoa pane is detemined b each object point ocation. On the conta, the affine image has no pojection cente. In the affine image the diection of pojected a is same fo an point on the image. Now consideing a a pojected fom an object point to an affine image, the epipoa pane can be defined as a pane in which the as of the two images ie. The

4 epipoa ine is an intesection ine between the affine image and the epipoa pane. In ode to geneate the epipoa images, each affine image can be pojected to a same vitua pane b paae pojection (Fig. 4, Fig. ). Let the vitua pane be a pane paae to the ight image. The image pojected on the pane fom ight image is identica to the ight image. On the condition, pojecting the eft image to the vitua pane is just same as pocessing affine tansfomation fom the eft image to the ight image. The eationship between the eft image point coodinates (, ) and the coesponding ight image point coodinates (, ) is simp descibed in the foowing fom: = K 1 = K (9) Fig. 3. We-Known Epipoa Geomet whee Ki (i = 1,,6) ae independent coefficients. Numbe of unknown paametes is 6 and numbe of independent equations is 2. Thus, if moe than 3 known points ae given, the equations can be soved. Anothe question is how to detemine the diection of the epipoa ine. Fo this pupose, we sha conside agebaic soutions of epipoa ine of affine images. As the autho has mentioned befoe, the basic equations of affine images ae descibed b equation and 6. These equations ae witten down fo a steeo pai of affine images in the fom: = A X + A Y + A Z + A 1 = A = A 2 6 = A X + A 2 X + A 6 3 X + A Y + A 7 Y + A 3 Y + A 7 4 Z + A 8 Z + A 4 Z + A 8 (10) Fig. 4. Epipoa Geomet of Affine Image B eiminating X and Y fom these equations and eaanging them, the eationship of the eft image point and the ight image point with change an object height Z is descibed as foows: = B 1 = B + B 2 + B 6 + B Z + B B Z + B 8 (11) B eiminating Z fom these equations, the epipoa ine of affine images is epessed in the fom: Fig.. Epipoa Resamping fom Affine Image

5 C1 + C2 + C3 + C4 = (12) Since numbe of unknown coefficients is 4 in Equation 12, moe than 4 known identica points coodinates between eft image and ight image ae equied fo the soution of this equation. The epipoa esamped images can be geneated b otating the vitua pane images b the ange coesponded to C1. Fina, in ode to geneate epipoa images fom affine images, a we need to know is the coodinates of moe than 4 identica points of the eft and ight affine images. The infomation such as the attitude of the images is not equied at a. 4.2 Appication to sateite image Since the actua sateite images ae not affine ones, the images shoud be appoimate tansfomed into affine ones b Equation 7 and 8. Equation 8 indicates that DTMs ae equied fo igoous tansfomation. As we sha see ate, howeve, we do not have to necessai use DTMs fo the pupose of epipoa esamping. The tansfomation eo in scanning diection causes vetica paaa (Fig. 6). In ode to avoid this pobem, the tansfomation shoud be caied out aong the epipoa ines instead of the scanning ines. Athough it is ve had to find the tue epipoa ines on the oigina image, the diection of the epipoa ine coesponding to the affine images can be detemined easi. The pocedues of epipoa esamping of sateite images ae as foows. 1. Appoimate, tansfom the oigina images to the affine ones aong scanning ine 2. Detemine the diection of the appoimate epipoa ines on the affine image 3. Tansfom the oigina images to the affine images aong the appoimate epipoa ines 4. Detemine the affine tansfomation coefficients (Equation 9). Ca out the affine tansfomation 6. Detemine the diection of the accuate epipoa ine 7. Rotate the affine tansfomed images b ange of the epipoa ine. Fig. 6. Vetica Paaa due to Tansfomation Eo into Affine Images The epipoa images ae geneated fom the affine images b using affine tansfomation. The epipoa image, that is, aso can be teated as anothe affine image. As mentioned in the pevious section, theefoe, 2D affine oientation mode can be diect appicabe to the epipoa images. The eationship between gound coodinates (X, Y, Z) of an object point and image coodinates (e, e) of the coesponding point on epipoa image ae descibed b same epession as Equation and 6. e e = D X + D Y + D Z + D 1 2 = D X + D Y + D Z + D (13) The coefficients Di ( i = 1,,8) ae detemined b the east squaes method with moe than 4 gound conto points data. Since the basic equations ae ve simpe, this method is appopiate fo ea time mapping of sateite image.

6 . PRACTICAL EVALUATION.1 Test Fied and Images good. But, the vetica paaa b this appoach was compaative age. It is ike that the geometic paametes wee not gotten accuac enough. Since unfotunate 1m high-esoution sateite images wee not avaiabe, the autho used a steeo pai of SPOT images in ode to investigate the chaacteistics of this method. Tabe-1 shows the condition of the test images. The steeo scene coves Hanshin aea (Osaka, Kobe and the sububs) in JAPAN. The southen aea of test fied is cit aea and amost fat. The nothen aea and the westen aea ae mountainous teain. The maimum height diffeence is about 1,000m. Fo the pupose of veification, 141 check points wee measued b manua. The measuement accuac of these points is 1/2 pie to 1/4 pie. 9 points among the check points ae used fo detemination of coefficients in basic equations (Equation 13). Fig.7 shows the test images and the distibution of the check points. Tabe-1 Test Image Data Left Image Right Image Image tpe SPOT pan Leve-1A Date Lat./Long. N34.7/E13. N32.7/E13.2 Incident ange L23.0 R17.9 B/H 0.7 Left Image.2 Resuts and Discussion In this stud, fou diffeent appoaches fo epipoa esamping wee evauated. 1. Otto s appoach which uses geometic oientation paametes 2. Poposed appoach, but diection of epipoa ine is not consideed. 3. Poposed appoach, but DTMs is used at tansfomation into affine images. 4. Poposed appoach The esuts obtained b these appoaches ae shown in Tabe-2. The accuac of Otto s appoach depends on that of oientation paametes. In this stud, Equation 1 was used as the coineait equations fo detemination of the oientation paametes. The changes of the paametes wee assumed to be inea, because non-inea mode isn t appopiate fo Otto s appoach. The RMSE in X,Y of the oientation was.1m and that in Z was 6.7m. This esut was ve Right Image Fig. 7. Test Images and Check Points Back points: check points White points: conto points On the conta, it seems that the poposed appoach woked efficient. The diffeent between the accuac of 2nd appoach and that of 4th appoach indicates that consideation of epipoa ine diection

7 is effective fo eduction of tansfomation eo due to negecting height diffeences. Besides, the poposed appoach without DTMs is no ess accuate than the case using DTMs. Fom these esuts, it can be concuded that epipoa esamping of sateite image in pactica accuac can achieve without DTMs b using the poposed method. Fo the efeence of discussion, the esuts of the oientation with 2D affine oientation mode ae shown in Tabe-3. We can see that appication of the 2D affine oientation mode is quite adequate fo the epipoa images. Tabe-2 Resuts of Each Appoach (pie) RMS of v-paaa Tabe-3 Resuts of Oientation (m) Oigina Images Epipoa Images σo ( 10 8 ) RMSE in X,Y RMSE in Z CONCLUSIONS The epipoa esamping appoach pesented in this pape is based on affine pojection image. This method is, theefoe, appopiate fo sma aea mapping with amost paae pojected image such as high-esoution sateite image. The poposed method does not equie DTMs o igoous geometic oientation paametes. In the pactica epeiments, it was shown that accuac bette than haf a pie was achieved b the poposed appoach. Futhemoe, since the esamping pocess is independent fom the oientation pocess and the basic equations of the oientation ae ve simpe, this method is appopiate fo ea time mapping. ACKNOWLEDGEMENTS The autho woud ike to dedicate this pape to the ate D. A. Okamoto, who had buit the fundation of this method and had given man advices. The autho aso wishes to thank to D. S.Hattoi and M. H. Hasegawa fo thei assistance with the pepaation of this pape. REFERENCES 1. G. P. Otto, Rectification of SPOT Data fo Steeo Image Matching, Intenationa Achives of Photogammet and Remote Sensing, Vo.27, B3, pp M. A. O Nei and I. J. Dowman, The Geneation of Epipoa Snthetic Steeo Mates fo SPOT Images Using a DEM, Intenationa Achives of Photogammet and Remote Sensing, Vo.27, B3, pp Nobet Haaa, Dik Stamann and Chistian Stätte, On The Use of Mutispecta and Steeo Data fom Aibone Scanning Sstems fo DTM Geneation and Landuse Cassification, Intenation Achives of Photogammet and Remote Sensing, Vo. 32, B4, pp T. Ono, A. Okamoto, S. Hattoi, H. Hasegawa, Fundamenta Anatic of Sateite CCD Camea Image Using Affine Tansfomation, Intenationa Achives of Photogammet and Remote Sensing, Vo.31, Commision III, pp A. Okamoto, C. Fase, S. Hattoi et a, An Atenative Appoach to the Tianguation of SPOT Image, Intenationa Achives of Photogammet and Remote Sensing, Vo.32, B4, pp A. Okamoto, T. Ono, S. Akamatsu et a, Geometic Chaacteistics of Atenative Tianguaion Modes fo Sateite Image, Poceedings of ASPRS 1999 Annua Confeence. 7. A. Okamoto, S. Akamatsu, H. Hasegawa, Oientation Theo fo Sateite CCD Line- Scanne Image of Hi Teains, Intenationa Achives of Photogammet and Remote Sensing, Vo.29, Commission II, pp O. Hofmann, Dnamische Photogammetie. BuL, Vo.4(), V. Katk, On-Line Aspects of Steeophotogammetic Pocessing of SPOT Images, Photogammetic Engineeing & Remote Sensing, Vo,(3),